Exporting / Importing Object with Animations
For this, you will have to do the animations in the 'dope sheet' tab.
If you still do not know, I'll show you how it works.
Basically, it is equal to timeline. But here, you can define several separate animations, and each one will have its own name.
To access the 'Dope sheet' tab, pull a new tab and select it.

Now you will have to switch to 'action editor', because this is where you can name animations and do other things.

Click New and type a name for your animation.

Check the F box so that the animations are saved in your project, so you will not risk losing them when you leave the blender and open the project again another time.

Now, do a little simple animation and export again to see if everything will work fine.
If you want to create more animations, just select + next to F.